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Parallelogram Calculator
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 Parallelogram calculator used to determine the area, perimeter and diagonal lengths of a parallelogram. It is an online mathematical tool for the easy calculation. The equation for the area, perimeter and diagonal lengths are mentioned below.Area= bh = absinθPerimeter = 2a+2bShort diagonal = $\sqrt{a^{2}+b^{2}-2abcos(\theta)}$Long diagonal = $\sqrt{a^{2}+b^{2}-2abcos(\pi -\theta )}$Where a and b are base lengths           h is the altitude           $\theta$ is the angle

## Steps for Parallelogram Calculator

Step 1 :

Identify the given parameters from the question.

Step 2 :

Area of a parallelogram is given as,

Area=absinθ

Step 3 :

Perimeter of a parallelogram is find out using the equation.

Perimeter=2a+2b

Step 4 :

Diagonal lengths are given by,

Short diagonal=$\sqrt{a^{2}+b^{2}-2abcos(\theta)}$

Long diagonal=$\sqrt{a^{2}+b^{2}-2abcos(\pi -\theta )}$

## Problems on Parallelogram Calculator

1. ### Determine the area, perimeter and diagonal lengths of a parallelogram whose a=3, b=4, h=8 and θ=$\pi$ rad?

Step 1 :

Given values are,

a=3, b=4, h=8 and θ=$\pi$ rad=180°

Step 2 :

Area=absinθ

Area=3×4×sin(180)

Area=-9.6138

Step 3 :

Perimeter=2a+2b

Perimeter=2×3+2×4=14

Step 4 :

Short diagonal=$\sqrt{a^{2}+b^{2}-2abcos(\theta)}$

Short diagonal=$\sqrt{3^{2}+4^{2}-2×3×4cos(180)}$=6.2739

Long diagonal=$\sqrt{a^{2}+b^{2}-2abcos(\pi -\theta )}$

Long diagonal=$\sqrt{3^{2}+4^{2}-2×3×4cos(0)}$=1

Area=-9.6138

Perimeter=14

Short diagonal=6.2739

Long diagonal=1

2. ### Find out the area, perimeter and diagonal lengths of a parallelogram whose a=5, b=8, h=10 and θ=$\pi$ rad?

Step 1 :

Given values are,

a=5, b=8, h=10 and θ=$\pi$ rad=180°

Step 2 :

Area=absinθ

Area=5×8×sin(180)

Area=-32.0461

Step 3 :

Perimeter=2a+2b

Perimeter=2×5+2×8=26

Step 4 :

Short diagonal=$\sqrt{a^{2}+b^{2}-2abcos(\theta)}$

Short diagonal=$\sqrt{5^{2}+8^{2}-2×5×8cos(180)}$=11.6994

Long diagonal=$\sqrt{a^{2}+b^{2}-2abcos(\pi -\theta )}$

Long diagonal=$\sqrt{5^{2}+8^{2}-2×5×8cos(0)}$=3